Characteristics of Measurement of Criterion Values and Adaptive - Digital Signal Processing in Power System Protection and Control - page 191

Fig. 9.14 Comparison of
measurement results of
a active power, b resistance
for various algorithms: 1—
standard, 2—with time delay,
3—with adaptation

(a)

0.5

3

P

0.4

0.3

0.2

2

1

0.1

100 125 150 175 200

t [ms]

(b)

R

1

1

2

0.8

0.6

3

0.4

100 125 150 175 200

t [ms]

for four percent of frequency deviation. It is seen that algorithms applying delayed
orthogonal components are much less sensitive to frequency deviations and, what
is very important for adaptive solutions errors, their responses are unique, phase
independent. Theoretical analysis of the situation may be interesting.
It is known that FIR orthogonal filters have output signals (for the same input)
which phase angles differ by p/2 at any arbitrary frequency. Then at given fre-
quency X the filter outputs can be expressed in the form:

y FC ð n Þ¼ H C ð jX Þ j j y C ð n Þ; ð 9 : 32a Þ

y FS ð n Þ¼ H S ð jX Þ

j j y S ð n Þ: ð 9 : 32b Þ

Let us calculate the function appearing in magnitude and active power algo-
rithms using outputs of the filters ( 9.32a , b ) (subscript F denotes output of the
filter, C, S stand for sine, cosine filter window, respectively):